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Analytical Fits to the Synchrotron Functions | M. Fouka
; S. Ouichaoui
; | Date: |
29 Jan 2013 | Abstract: | Accurate fitting formulae to the synchrotron function, $F(x)$, and its
complementary function, $G(x)$, are performed and presented. The corresponding
relative errors are less than $0.26\%$ and $0.035\%$ for $F(x) $ and $G(x)$,
respectively. To this aim we have, first, fitted the modified Bessel functions,
$K_{5/3}(x)$ and $K_{2/3}(x)$. For all the fitted functions, the general fit
expression is the same, and is based on the well known asymptotic forms for low
and large $x$-values for each function. It consists of multiplying each
asymptotic form by a function that tends to unity or zero for low and large
$x$-values. Simple formulae are suggested in this paper, depending on
adjustable parameters. The latter have been determined by adopting the
Levenberg-Marquardt algorithm. The proposed formulae should be of great utility
and simplicity for computing spectral powers and the degree of polarization for
the synchrotron radiation, both for laboratory and astrophysical applications. | Source: | arXiv, 1301.6908 | Services: | Forum | Review | PDF | Favorites |
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